A Beginner's Guide to Options Pricing

Time decay works in favor of option sellers and against option buyers

Jun 29, 2017 at 3:24 PM
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    Option pricing is calculated using the Black-Scholes model, which takes four influential factors into account: the price of an underlying stock (assuming constant drift and volatility), an option’s strike price, the amount of time until the option expires, and a constant, risk-free interest rate. Today, we’ll dive into two of these option pricing influences: intrinsic value and time value.

    Intrinsic Value

    Intrinsic value is the difference between the underlying stock’s current market price and the option’s strike price. Only in-the-money options carry intrinsic value. A call option is in the money when the stock price exceeds the strike price, whereas a put option is in the money when the stock price falls below the strike price.

    To find the intrinsic value of a call option, subtract the strike price from the stock price. Do the opposite to find the intrinsic value of a put option.

    For example, if you buy a 100-strike call option and the underlying stock price rises to $110 before the option’s expiration date, the intrinsic value of your in-the-money call option would be $10 (110 - 100 = $10). If you buy a 100-strike put option and the underlying stock price drops to $90, the intrinsic value of your in-the-money put option would also be $10 (100 - 90 = $10).

    Time Value

    Time value, also called extrinsic value, is based on the time an option has until expiration and its implied volatility. The more time an option has until expiration, the greater time value it carries.

    Hypothetically, more time allows in-the-money options to increase in intrinsic value, and out-of-the-money or at-the-money options to move into the money. Since longer-term options buy traders time for the underlying stock to move as they expected, options with greater time value cost more. An October XYZ 100 put option, for example, would cost more than a July XYZ 100 put, because the October option allows more time for the stock price to move lower than the strike price.  

    At-the-money and out-of-the-money options are comprised of only time value, since they can't harbor intrinsic value. Call and put options are at the money when the stock price equals the strike price. Call options are out of the money when the stock price falls below the strike price; the opposite is true for put options.

    Time Decay

    An option’s time value decreases as it approaches its expiration date. We call this time decay. As an option’s expiration date nears, the rate of time decay increases. Thus, time decay works in favor of an option seller and against an option buyer. This is because time decay allots option buyers less time for the underlying stock to move as they expected, and a lower extrinsic value translates into a cheaper option contract, which means a smaller profit gain for option buyers able to liquidate their positions.

    Option sellers are in favor of time decay, though, as their goal is usually for the option to remain out of the money through expiration, rendering the option worthless and allowing them to pocket the initial premium received.   

    An option is only worth its intrinsic value upon expiration. Thus, at-the-money and out-of-the-money options are worth nothing at expiration, since neither carry intrinsic value.

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